Abstract
The Bogoliubov transformation in cosmological particle production can be explained by the Stokes phenomena of the corresponding ordinary differential equation. The calculation becomes very simple as far as the solution is described by a special function. Otherwise, the calculation requires more tactics, where the Exact WKB (EWKB) may be a powerful tool. Using the EWKB, we discuss cosmological particle production focusing on the effect of more general interaction and classical scattering. The classical scattering appears when the corresponding scattering problem of the Schrödinger equation develops classical turning points on the trajectory. The higher process of fermionic preheating is also discussed using the Landau-Zener model.
Highlights
If one replaces φ(t) with φ(t) vt, the above equation is equivalent to the Schrödinger equation of the scattering problem by the “inverted quadratic potential” given by
Using the Exact WKB (EWKB), we discuss cosmological particle production focusing on the effect of more general interaction and classical scattering
The EWKB is a powerful tool for calculating the connection formula, especially useful when the entire solution cannot be transformed into a special function
Summary
We describe the calculation based on the EWKB analysis, which gives a simple method for calculating the connection formula. Note that the normalization problem is typical in the ordinary WKB method, which can be avoided by putting consistency conditions [5]. [14, 22, 23] for typical MTP (Merged pair of simple Turning Points). In this case, the factor has to be introduced on both sides of each MTP structure. We note here that for the simple example discussed here (i.e, scattering with an inverted quadratic potential), the exact solution is already known as the Weber function and there is no obvious merit for considering alternative formulation.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
